CONCORD — With another team, Coach Tim Walsh knew, the Bow boys’ hockey team’s season would have been in trouble.

The Falcons trailed old nemesis Dover by a goal late in the Division II quarterfinals, and though just under 20 minutes of game time remained, it was a spot for a weaker team to get down on itself and start to give up and give in.

“A year ago, this game would have been over,” Walsh said. “We would have lost 3-1. This year, we’ve really learned how to win.”

The fourth-seeded Falcons got chances to show it when a pair of power plays gave them life, and they converted on both en route to a 4-2 victory, their first-ever postseason win over the No. 5 Green Wave.

“The kids have grown, they’ve matured, they’ve become very mature on the ice in terms of how to adjust to adversity,” Walsh said. “We win very few blowout games. A lot of our games are close games. That helps in the playoffs. The kids knew how to react.”

Bow had to show that poise after Ben Henderson fired home a rebound to put Dover (11-7-1) up 2-1 with 10:56 left in the second, but the Green Wave made it easier when it was whistled for its fourth penalty of the period with 3:38 to go. The Falcons needed less than a minute to cash in, as they brought the puck up and crashed the net and Fournier chipped in the loose puck to knot the score with 2:46 left.

Soon after the third period began, a hooking call put the Falcons on the man advantage again, and they again made the Green Wave pay. Jake Rand threw the puck in from the point and Derek Tillotson corralled it, and though his shot was saved, Fournier was again in position to swoop in and knock in the rebound for the 3-2 lead with 12:42 left.

“I saw the puck go at the net and I saw (Tillotson), he was going at it and I thought he was going to put the puck in. It went off the goalie’s pad and it went right to me,” said Fournier, whose team got its final goal on a Rand empty-netter with 3.8 seconds left. “Knowing that we got that lead, it was great.”

There was time left for Dover to make a push, but the Green Wave had trouble mustering an attack the rest of the way. Bow held Dover to just three shots in the period, and none after the Green Wave pulled its goalie with 1:14 left, and Coach Steve Riker said spending chunks of the game late on the penalty kill may have sapped his team of its energy.

“I thought today’s game was just a microcosm of our season,” he said. “We had a hard time this year staying out of the penalty box. It’s tough to play shorthanded. Not only does it give the other team an opportunity to score, but now you’re wearing your guys out. … Maybe if we don’t take all those penalties in the second, maybe we make a better push in the third.”

Bow grabbed a 1-0 lead with 11:43 to go in the first when Hunter Berke won a faceoff and Fournier took the puck, wheeled around and fired a wrist shot through traffic that beat goalie Luc Ravenelle (27 saves). Dover tied the game with 5:48 left in the first, when Alec Parmer put a shot on goal and, after a save by Connor Simpson (15 saves), Joe Johnston was in position to stuff in the rebound.

The game was the latest chapter in what had been an intense rivalry, as Dover beat Bow in three straight semifinals from 2004-06, but though the personal nature of the games had diminished, Walsh said his team still knew to respect the team that had made the last two championship games and won it all in 2011.

“Dover always typically raises their level in the playoffs,” he said. “They always do. That’s what they’ve done. They know how to win.”

So does Bow’s next opponent, Merrimack, which has won 17 of the 19 games it’s played this season.

“We can’t let up for a second,” Walsh said. “No matter what the score is, no matter what the situation is. … They can score four goals in a minute. We have to stay focused for 45 minutes.”